21 research outputs found
Mechanics of diffusion-mediated budding and implications for virus replication and infection
Budding allows virus replication and macromolecular secretion in cells. It
involves the formation of a bud, i.e. an outgrowth from the cell membrane that
evolves into an envelope. The largest energetic barrier to bud formation is
membrane deflection and is trespassed primarily thanks to nucleocapsid-membrane
adhesion. Transmembrane proteins (TPs), which later form the virus ligands, are
the main promotors of adhesion and can accommodate membrane bending thanks to
an induced spontaneous curvature. Adhesive TPs must diffuse across the membrane
from remote regions to gather on the bud surface, thus, diffusivity controls
the kinetics. This paper proposes a simple model to describe diffusion-mediated
budding unraveling important size limitations and size-dependent kinetics. The
predicted optimal virion radius, giving the fastest budding, is validated
against experiments for Coronavirus, HIV, Flu, and Hepatitis. Assuming
exponential replication of virions and hereditary size, the model can predict
the size distribution of a virus population. This is verified against
experiments for SARS-CoV-2. All the above comparisons rely on the premise that
budding poses the tightest size constraint. This is true in most cases, as
demonstrated in this paper, where the proposed model is extended to describe
virus infection via receptor- and clathrin-mediated endocytosis, and via
membrane fusion
Multi-material topology optimization of adhesive backing layers via J-integral and strain energy minimizations
Strong adhesives rely on reduced stress concentrations, often obtained via
specific geometry or composition of materials. In many examples in nature and
engineering prototypes, the adhesive performance relies on structural rigidity
being placed in specific locations. A few design principles have been
formulated, based on parametric optimization, while a general design tool is
still missing. We propose to use topology optimization to achieve optimal
stiffness distribution in a multi-material adhesive backing layer, reducing
stress concentration at specified locations. The method involves the
minimization of a linear combination of J-integral and strain energy. While the
J-integral minimization is aimed at reducing stress concentration, we observe
that the combination of these two objectives ultimately provides the best
results. We analyze three cases in plane strain conditions, namely (i)
double-edged crack and (ii) center crack in tension and (iii) edge crack under
shear. Each case evidences a different optimal topology with (i) and (ii)
providing similar results. The optimal topology allocates stiffness in regions
that are far away from the crack tip, intuitively, but the allocation of softer
materials over stiffer ones can be non-trivial. To test our solutions, we plot
the contact stress distribution across the interface. In all observed cases, we
eliminate the stress singularity at the crack tip. Stress concentrations might
arise in locations far away from the crack tip, but the final results are
independent of crack size. Our method ultimately provides optimal, flaw
tolerant, adhesives where the crack location is known
Making the cut: end effects and the benefits of slicing
Cutting mechanics in soft solids have been a subject of study for several
decades, an interest fuelled by the multitude of its applications, including
material testing, manufacturing, and biomedical technology. Wire cutting is the
simplest model system to analyze the cutting resistance of a soft material.
However, even for this simple system, the complex failure mechanisms that
underpin cutting are still not completely understood. Several models that
connect the critical cutting force to the radius of the wire and the key
mechanical properties of the cut material have been proposed. An almost
ubiquitous simplifying assumption is a state of plane (and anti-plane) strain
in the material. In this paper, we show that this assumption can lead to
erroneous conclusions because even such a simple cutting problem is essentially
three-dimensional. A planar approximation restricts the analysis to the stress
distribution in the mid-plane. However, through finite element modeling, we
reveal that the maximal tensile stress - and thus the likely location of cut
initiation - is in fact located in the front plane. Friction reduces the
magnitude of this stress, but this detrimental effect can be counteracted by
large slice-to-push (shear-to-indentation) ratios. The introduction of these
end effects helps reconcile a recent controversy around the role of friction in
wire cutting, for it implies that slicing can indeed reduce required cutting
forces, but only if the slice-push ratio and the friction coefficient are
sufficiently large. Material strain-stiffening reduces the critical indentation
depth required to initiate the cut further and thus needs to be considered when
cutting non-linearly elastic materials
Theoretical Puncture Mechanics of Soft Compressible Solids
Accurate prediction of the force required to puncture a soft material is
critical in many fields like medical technology, food processing, and
manufacturing. However, such a prediction strongly depends on our understanding
of the complex nonlinear behavior of the material subject to deep indentation
and complex failure mechanisms. Only recently we developed theories capable of
correlating puncture force with material properties and needle geometry.
However, such models are based on simplifications that seldom limit their
applicability to real cases. One common assumption is the incompressibility of
the cut material, albeit no material is truly incompressible. In this paper we
propose a simple model that accounts for linearly elastic compressibility, and
its interplay with toughness, stiffness, and elastic strain-stiffening.
Confirming previous theories and experiments, materials having high-toughness
and low-modulus exhibit the highest puncture resistance at a given needle
radius. Surprisingly, in these conditions, we observe that incompressible
materials exhibit the lowest puncture resistance, where volumetric
compressibility can create an additional (strain) energy barrier to puncture.
Our model provides a valuable tool to assess the puncture resistance of soft
compressible materials and suggests new design strategies for sharp needles and
puncture-resistant materials
Energetics of Cytoskeletal Gel Contraction
Cytoskeletal gels are prototyped to reproduce the mechanical contraction of
the cytoskeleton in-vitro. They are composed of a polymer network (backbone),
swollen by the presence of a liquid solvent, and active molecules (molecular
motors, MMs) that transduce chemical energy into the mechanical work of
contraction. These motors attach to the polymer chains to shorten them and/or
act as dynamic crosslinks, thereby constraining the thermal fluctuation of the
chains. We describe both mechanisms thermodynamically as a microstructural
reconfiguration, where the backbone stiffens to motivate solvent (out)flow and
accommodate contraction. Via simple steady-state energetic analysis, under the
simplest case of isotropic contraction, we quantify the mechanical energy
required to achieve contraction as a function of polymer chain density and
molecular motor density. We identify two limit cases, (fm) fast MM activation
for which MMs provide all the available mechanical energy instantaneously and
leave the polymer in a stiffened state, i.e. their activity occurs at a time
scale that is much smaller than solvent diffusion, and (sm) slow MM activation
for which the MM activation timescale is much longer. To achieve the same final
contracted state, fm requires the largest amount of work per unit reference
volume, while sm requires the least. For all intermediate cases where the
timescale of MM activation is comparable with that of solvent flow, the
required work ranges between the two cases. We provide all these quantities as
a function of chain density and MM density. Finally, we compare our results
with experiments and observe good agreement
Homogenization of heterogeneous Cauchy-elastic materials leads to Mindlin second-gradient elasticity
Through a second-order homogenization procedure, the explicit relation is obtained between the non-local parameters of a second gradient elastic ma- terial and the microstructure of a composite material. This result is instru- mental for the definition of higher-order models, to be used for the analysis of mechanics at micro- and nano-scale, where size-effects become important.
The obtained relation is valid for both plane and three-dimensional prob- lems and generalizes earlier findings by Bigoni and Drugan (Analytical deriva- tion of Cosserat moduli via homogenization of heterogeneous elastic materials. J. Appl. Mech., 2007, 74, 741753) from several points of view:
i) the result holds for anisotropic phases with spherical or circular ellipsoid of inertia;
ii) the displacement boundary conditions considered in the homogenization procedure is independent of the characteristics of the material;
iii) a perfect energy match is found between heterogeneous and equivalent materials (instead of an optimal bound).
From the obtained solution it follows that the equivalent second-gradient Mindlin elastic solid:
a) is positive definite only when the discrepancy tensor is negative defined;
b) the non-local material symmetries are the same of the discrepancy tensor;
c) the non-local effective behaviour is affected by the shape of the RVE, which does not influence the first-order homogenized response.
Finally, explicit derivations of non-local parameters from heterogeneous Cauchy elastic composites are obtained in particular cases